This paper deals with mixed H2infinty H1 state feedback control applied to mechanical systems. The H1 infinty constraint allows to specify disturbance rejection performance on the acceleration sensibility function while the H2infinty optimization allows to minimize the energy consumption. In the one d.o.f. case, optimality conditions are derived literally to interpret the various admissible solutions according to the frequency response of the weighted open-loop acceleration sensibility function, that is: on the frequency range where the disturbance rejection performance must be increased by the control law. Solutions to this problem in the multi-variable case using numerical solvers are discussed. Some illustrative examples, including aircraft lateral flight control laws, are proposed to highlight main results
